Solution to problem 20.6.17 from the collection of Kepe O.E.

20.6.17 In a mechanics problem, you need to find the generalized acceleration x of a conservative mechanical system with one degree of freedom at the time when x equals 2m. To do this, it is necessary to use the kinetic potential formula, which for a given system takes the form L = 4x² - x⁴ - 6x². Having solved the problem, we get the answer: 7.

Write a description of the product - a digital product in a digital goods store with a beautiful html design: "Solution to problem 20.6.17 from the collection of Kepe O.?."

We present to you a digital product in the digital goods store - “Solution to problem 20.6.17 from the collection of Kepe O.?”. This product provides a detailed solution to a mechanical problem that requires finding the generalized acceleration x of a conservative mechanical system with one degree of freedom at the time when x equals 2m. To solve the problem, it is necessary to use the kinetic potential formula, which for a given system takes the form L = 4x² - x⁴ - 6x². The entire product solution is presented in a beautiful html design, which makes it easy to use and allows you to quickly and accurately find the necessary information. The answer to the problem in this case is 7.

I offer you a digital product - a solution to problem 20.6.17 from the collection of Kepe O.?. in mechanics. This product contains a detailed description of the process of solving this problem, designed in a beautiful html format.

The problem requires finding the generalized acceleration x of a conservative mechanical system with one degree of freedom at the time when x equals 2m. To solve, the formula for the kinetic potential L is used, which for a given system takes the form L = 4x² - x⁴ - 6x².

By purchasing this product, you will receive a complete solution to the problem with a step-by-step description of the formulas and solution methods used. And also, you will receive an answer to this problem, which is 7.

***

Solution to problem 20.6.17 from the collection of Kepe O.?. consists in determining the generalized acceleration x at the moment of time when x = 2 meters, for a conservative mechanical system with one degree of freedom, in which the kinetic potential is given by the expression L = 4x^2 - x^4 - 6x^2, where x is the generalized coordinate .

To solve the problem, it is necessary to find the Lagrange equation of the second kind, then calculate the generalized forces equal to the derivative of the Lagrange equation with respect to the generalized coordinate, and substitute the value of the coordinate x = 2 meters into the resulting equation. As a result, we obtain the value of the generalized acceleration x at the moment of time when x = 2 meters, which is equal to 7.

Thus, to solve this problem, you must complete the following steps:

1. Find the Lagrange equation of the second kind, which has the form:

Lagrange = d/dt(dL/dx_dot) - dL/dx,

where L is the kinetic potential of the system, x_dot is the derivative of the generalized coordinate with respect to time.

1. Calculate the derivative of the kinetic potential with respect to speed:

dL/dx_dot = 8x_dot - 4x_dot^3

1. Calculate the derivative of the kinetic potential with respect to the coordinate:

dL/dx = 8x - 4x^3 - 12x

1. Substitute the obtained values ​​into the Lagrange equation of the second kind:

Lagrange = d/dt(8x_dot - 4x_dot^3) - (8x - 4x^3 - 12x)

1. Calculate the time derivative of the derivative of the generalized velocity:

d/dt(dL/dx_dot) = d^2x/dt^2(8 - 12x^2)

1. Substitute the obtained values ​​into the Lagrange equation of the second kind:

d^2x/dt^2(8 - 12x^2) - (8x - 4x^3 - 12x) = 0

1. Solve the resulting differential equation using the initial conditions specified in the problem statement.

2. Substitute the value x = 2 meters into the resulting solution and calculate the generalized acceleration x at the time when x = 2 meters. The answer should be 7.

Thus, the solution to problem 20.6.17 from the collection of Kepe O.?. consists in finding the generalized acceleration x at the time when x = 2 meters, for a conservative mechanical system with one degree of freedom, whose kinetic potential is given by the expression L = 4x^2 - x^4 - 6x^2.

***

1. This digital product helped me successfully solve the problem from the collection of Kepe O.E.
2. Great solution to the problem that I got from this digital product.
3. I was very pleased with this digital product, it helped me with my exam.
4. Thank you for this digital product, it helped me understand the material better.
5. I would recommend this digital product to anyone looking for help with Kepe's problems.
6. An excellent digital product that helped me save time and complete a task faster.
7. A very useful digital product, I was able to easily understand the material thanks to it.
8. A very useful digital product for those studying physics. Solution to problem 20.6.17 from the collection of Kepe O.E. helps to better understand the topic and master the material.
9. Solution to problem 20.6.17 from the collection of Kepe O.E. - This is an excellent tool for independent study of physics. The solution is accompanied by detailed explanations and drawings.
10. A quick and high-quality solution to problem 20.6.17 from the collection of Kepe O.E. Thanks to the author for the excellent work!
11. Solution to problem 20.6.17 from the collection of Kepe O.E. helped me prepare for my physics exam. I highly recommend it to all students and schoolchildren who are studying this subject.
12. I am grateful to the author for solving problem 20.6.17 from the collection of Kepe O.E. This helped me understand the topic better and prepare for the exam.
13. Solution to problem 20.6.17 from the collection of Kepe O.E. is an excellent digital product for those who study physics on their own. The solution is easy to read and understand.
14. Thanks to the author for solving problem 20.6.17 from the collection of Kepe O.E. Very good quality and affordable price.

Peculiarities:

Solution of problem 20.6.17 from the collection of Kepe O.E. helped me a lot in my math studies.

I am very grateful to the author for such an excellent collection of problems, which also contains problem 20.6.17.

Solution of problem 20.6.17 from the collection of Kepe O.E. was very clear and accessible to me.

By solving problem 20.6.17 from the collection of Kepe O.E. I understood the material better.

Solution of problem 20.6.17 from the collection of Kepe O.E. very helpful in preparing for the exam.

I quickly figured out the solution of problem 20.6.17 from the collection of Kepe O.E. thanks to the clear presentation of the author.

By solving problem 20.6.17 from the collection of Kepe O.E. I was able to improve my level of knowledge in mathematics.

Solution of problem 20.6.17 from the collection of Kepe O.E. was helpful as I could test my knowledge on my own.

I am grateful to the author for solving problem 20.6.17 from O.E. Kepe's collection, as it helped me to better understand the topic.

By solving problem 20.6.17 from the collection of Kepe O.E. I was able to consolidate my knowledge in mathematics.